I think the first thing you should do is to talk to your neighbor about it. Instead of making extra work for yourself and potential creating a hostile neighbor, which no one likes, you should just go talk to your neighbor an tell them you intend to put up a fence. Be nice and explain that they have a shrub growing over the property line and that it needs to be trimmed back for the fence. Show them where the property line goes and how much of the plant you need trimmed back and ask them if they'd like to cut it or would they like you to.
Chances are, they won't trust you to get it as pretty as they like and will do the work for you. Even if a few wisps still stick onto your side, you can snip them off or just let them rub against the fence. If they say for you to, then try to do a descent job of it and if they don't like it, they can't complain.
If they try to pitch a fit and say you aren't touching their tree, then politely inform them of what the local law says about your ability to trim plants that encroach on your property and that you were trying to be friendly about it. If they keep on, don't argue, just go do what you need to do, to legally trim it up. Good luck.